The present invention relates to, inter alia, noise extraction from a signal. The signal may be used, for example, in the generation of images from projection measurements. Examples of images generated from projection measurements include two-dimensional and three-dimensional SAR (synthetic aperture radar) systems, such as that disclosed in U.S. Pat. No. 5,805,098 to McCorkle, hereby incorporated by reference, wherein an aircraft mounted detector array is utilized to take ground radar measurements. Other examples of systems relating to noise extraction from a signal include fault inspection systems using acoustic imaging, submarine sonar for imaging underwater objects, imaging systems for tunnel detection, oil exploration, geological surveys, etc., and medical diagnostic tools such as sonograms, echocardiograms, x-ray CAT (computer-aided tomography) equipment and MRI (magnetic resonance imaging) equipment.
The U.S. Army has been developing low-frequency ultra-wideband systems to detect targets in foliage, explosive devices buried in the ground, moving targets behind walls or barriers (sensing-through-the-wall). Such systems operate in the low-frequency spectrum than spans from under 100 MHz to several GHz in order to have penetration capability while maintaining high image resolution. Therefore, these systems must operate in the low-frequency spectrum that spans from under 100 MHz to several GHz in order to achieve the penetration capability. A critical challenge for ultra-wideband radar is that collected radar information is corrupted in both the time and frequency domain by radio frequency interference (RFI) signals within the operating spectrum of UWB radar, as the signal occupies a wide spectrum that is also shared by radio, TV, cellular phone, wireless networking, amateur radio and other systems. Because of this interference, the received signal contains spectral content that includes many frequency subbands that are corrupted by energy from all other sources. Within these corrupted subbands, the energy of the received signal is much smaller than that from the interference sources, since the interfering signals are essentially large amplitude noise that often masks the underlying radar signals. In the time domain, the signal is very noisy and might be embedded in the noise floor. Except for targets with very large amplitudes, targets may not be detectable in the presence of interference noise. Conventional techniques usually detect the corrupted frequency bands (due to the interference sources) by searching for the spikes in the spectral domain. The fast Fourier transform (FFT) bins that correspond to the contaminated frequency bands are zeroed out. This technique results in severe sidelobes in the time or spatial domain of the output data and imagery due to the sharp transitions (frequency samples with no information) in the frequency domain. In addition, simply suppressing the information in the contaminated frequency bands will reduce the signal-to-noise ratio (SNR) of the received signal.
One noise suppression technique that has been widely employed in practice involves implementing adaptive notch filters (whose notches in the frequency domain correspond to interference noise components) to suppress the energy from interference noise signals. Depending on the nature of interference noise sources, the notch-filter approach generally results in (i) large sidelobes in the time domain of the received signal and (ii) reduced target amplitudes since our transmitted radar signals are UWB and notching partially eliminates the radar signals of interest. It is generally more desirable to extract the interference noise from signal directly in the time domain for best performance. To avoid the side effects of the notch-filter implementation, Timothy Miller, et al., in the publication entitled “RFI Suppression for Ultra Wideband Radar,” IEEE Transactions on Aerospace and Electronic Systems, vol. 33, no. 4, (October 1997) (herein incorporated by reference) proposed an interference noise suppression technique that estimates the noise components and subtracts (in the time domain) the estimated noise signal from the received radar signal. However, the technique requires complete knowledge of the interference sources. The technique is based on the assumption that the interference sources consist of a number of narrowband amplitude modulation (AM) and frequency modulation (FM) channels. This assumption is no longer valid with the current frequency spectrum, in which most of the communications and TV channels are broadcasting using various digital modulation schemes. Within each communications channel, the radio frequency (RF) signal looks like white noise in the time domain with its amplitude and phase quickly varying with respect to time. Thus, it is not practical to use the Miller technique to estimate these RF interference (RFI) components with digital modulation contents. Besides parametric noise modeling, spectral decomposition, and adaptive filtering have also been explored to solve the RFI problem and so far have yielded limited successes. Most can only provide acceptable results with one particular source of RFI.